Davolos_Lab 5

Rowan Introduction to Astronomy —— S ——— — Lab 5/ Properties of Telescopes: Light-Gathering Power, Magnification, Resolution Name: ¥ ®en Yo lof P ASummary: The student will learn about the relationship between objective size, resolution, focal length, and magnification.. ALight-Gathering Power [33 pts] Light-gathering power of a telescope is directly proportional to the area of its primary lens or mirror. All lenses and mirrors have a circular circumference. The arca of a circle is given by the formula: 4 = nr?. Because 7 is a constant, the radius, 7, of the mirror or lens is the most important factor in determining the light-gathering power of a telescope. Note that area of a circle varies by the square of the radius. Thus, a lens or mirror that is twice the radius (or diameter) of another telescope objective has 2 or 4 times the light- gathering power. 1. A typical pair of binoculars has an objective lens of 50-mm diameter. A typical amateur telescope is an 8-inch reflector that has a mirror diameter of 203 mm. (Give answers in and b as a number: that is, when multiplying, use x as 3.14159.) (2) What is the light-collecting area of the S0-mm objective? \ 0\ 621 g (b) What is the light-collecting area of the 203-mm objective? % 7' zésl (4 (c) The 203-mm objective collects l times the light of a 50-mm objective. | (d) The brightness of celestial objects usually is expressed in terms of magnitude. A 1% magnitude star is defined as being 100 times brighter than a 6™ magnitude star (5 magnitude steps). A single magnitude jump equals a brightness change of about 2.512 (given that 2.512% = 100). Using the factor of 2.512 for a single magnitude 'umg,q_gbout ‘how many magnitudes fainter can the 203-mm objective “see” than the smaller 50-mm objective? [R neares 1be ; magnitudes [Hint: 2.512' =2.512; 2.5122=9; 2.512%=17;2.5124=2,25125= 100] %ical “4-inch” telescope, usuallg & refi‘actor) with that of the Keck tel 2. Compare 2n amateur telescope of 100 mm which is 10 meters across. Work s of ten; 2. (2) Area of 100-mm objective in mm?: 3 , ‘{Z Y, 7 mm?® Area of 100-mm objective in m* 3» 0w (Careful! Note the conversion from millimeters® to meters®. Workine with powers of ten can make this step easier. Hint: How many mm in | meter? How many mm? in 1 m*?) [Round 2 decimals (c) Area of 10-m Keck objective: 3\ T & (d) 10-m objective collects l,b 0 Q) S) times the light of a 100-mm objective [Rl (¢) The answer to (d) represents how many magnitudes? (Hint: Look for the x* function on a scientific calculator. If(2.512)* = 100 and represents 3 magnitude steps, then how many steps does the answer to d represent? If 100 = 10 X 10 or 10, then how many powers of ten is the ans.wer to d?) (b ~ 3. A quicker way 1o calculate light-gathering power is to use the formula: Lp, (p,) LGp, \D, where LGP, and LGPy are the light-gathering powers of A and B respectively, g ! and B, respectively. If the human eye has a diameter of § mm (actuall)l') the puglzld:;lthDA and Dy and a 203-mm telescope, how much more light will the telescopes gather than R eyef‘:? ?Y?? (a) LGP e = o : . : mm_ bl P = 3D 0 [ times more ight (®) LGPaymy LGP, - M . times more light

Lab 5/ Properties of Telescopes: Light-Gathering Power, Magnification, Resol _AMagnification [37 pts: 36 pts + 1 “free” pt] lescope to enlarge an image. Though usually the most well-known, due to the telescope and particularly of an optical instrument such as a te elescope because it enlar ccause they are points o ded objects such as planets or clusters can b lose to Earth, the planets in our solar system show as a disk rather than as a ges any distortions flight. (The disk of a star image under magnification is Magnification is the ability enefit from some magnification magnifying power is the least important function of a t the atmosphere. Magnification does not work on stars b just the light from the star smeared out.). However, exten under good seeing conditions. Because they are relatively ¢ point of light. We can magnify that disk to see more detail. useful power is about 60X per inch of objective aperture. Thus, a 4-inch (102-mm) 4-mm) can handle 480X. Thus, the claim that a cheap 60-mm (2.4-inch) refractor can q Under the best sky conditions possible, the top practical usage under typical skies, most telescopes work telescope can handle at best 240X, An 8-inch (25 provide “600X" is false. At best, a 60-mm objective can handle 144X, For best at magnifications in the range of 10X ~30X per inch of aperture. dependent on two factors: the focal length of the telescope—the objective lens or for calculating magnification The magnification a telescope can provide is d 1o complete the telescope optical system. The formula mirror— and the focal length of the eyepiece use: is given below: magnification = fop/feve where fa is the focal length of the objective and f. is the focal length of the eyepiece. (Eyepiece focal lengths always appear on the barrel of the eyepicce.) The “speed” (or “f* number) of a telescope is determined by dividing the focal length of the objective by the diameter of the objective (usually in millimeters). For example, a refractor with a 150-mm (6-inch) diameter objective and a 1200-mrm focal length has a speed of £8. A reflector with a 256-mm (10-inch) diameter and a 1200-mm focal length has a speed of /4.7. The reflector is said to be “faster” than the refractor. Fast focal length telescopes are good for observi laxi d othier fainit deep space objects. Telescopes with slower focal lengths are good for observing planets. fiqfi: length earest w mber.] r f/obj = fos/dub; J 735 Telescope 1: William Optics 105-mm (4.1-inch) £/7 refractor. The focal length of this telescope is: Telescope 2: Orion Telescopes 203-mm (8-inch) /5.91 reflector. The focal length of this telescope is: ’ , 7 o 7, g mm ; 280 3 Telescope 3: Celestron 279-mm (11-inch) /10 Schmidt-Cassegrain. The focal length of this telescope is: [Each answer above is worth 2 pts for a total of 6 pts.] Given the eyepiece in column 1, fill in the magnification for each telescope with that eyepiece. m [Each correctly filled-in blank in the table is worth 0.75 pt for a total of 21 pts.] [ Eyepiece f.I. Telescope 1 Telescope 2 Telescope 3 3 mm 245 Y460 26 4 o L ¥4 300 £y 6 mm | 2.2 260 ¢ LS 9mm 82 (?; g/o 12 mm é( 100 ’L?Z 15 mm “Hd %0 L%@ 18 mm Yl 67 lSS 20 mm A & O lq () 25 mm U[ yy% ”rL 87 32 mm ,L’; '57 P